Two Formulas for the General Multivariate Polynomial Which Interpolates a Regular Grid on a Simplex
نویسندگان
چکیده
Two formulas are exhibited for the multivariate Lagrange shape polynomials which interpolate a regular grid on a simplex in R".
منابع مشابه
An Error Analysis for Polynomial Optimization over the Simplex Based on the Multivariate Hypergeometric Distribution
We study the minimization of fixed-degree polynomials over the simplex. This problem is well-known to be NP-hard, as it contains the maximum stable set problem in graph theory as a special case. In this paper, we consider a rational approximation by taking the minimum over the regular grid, which consists of rational points with denominator r (for given r). We show that the associated convergen...
متن کاملA refined error analysis for fixed-degree polynomial optimization over the simplex
We consider the problem of minimizing a fixed-degree polynomial over the standard simplex. This problem is well known to be NP-hard, since it contains the maximum stable set problem in combinatorial optimization as a special case. In this paper, we revisit a known upper bound obtained by taking the minimum value on a regular grid, and a known lower bound based on Pólya’s representation theorem....
متن کاملgH-differentiable of the 2th-order functions interpolating
Fuzzy Hermite interpolation of 5th degree generalizes Lagrange interpolation by fitting a polynomial to a function f that not only interpolates f at each knot but also interpolates two number of consecutive Generalized Hukuhara derivatives of f at each knot. The provided solution for the 5th degree fuzzy Hermite interpolation problem in this paper is based on cardinal basis functions linear com...
متن کاملGenerating dimension formulas for multivariate splines
Dimensions of spaces of multivariate splines remain unknown in general. A computational method to obtain explicit formulas for the dimension of spline spaces on simplicial partitions is described. The method is based on Hilbert series and Hilbert polynomials. It is applied to conjecture the dimension formulas for splines on the Alfeld split of a simplex and on several other partitions. AMS clas...
متن کاملOn the convergence rate of grid search for polynomial optimization over the simplex
We consider the approximate minimization of a given polynomial on the standard simplex, obtained by taking the minimum value over all rational grid points with given denominator r ∈ N. It was shown in [De Klerk, E., Laurent, M., Sun, Z.: An error analysis for polynomial optimization over the simplex based on the multivariate hypergeometric distribution. SIAM J. Optim. 25(3) 1498–1514 (2015)] th...
متن کامل